Recent scientific advances, such as the development of sensitive measures of viral burden and the ability to sequence virus, have produced powerful new tools for understanding and controlling the HIV epidemic. In addition, treatment advances make it often possible to reduce viral burden below levels of detection. While these development increase the possibilities for epidemic control, new statistical methods are required to make full use of them. Treatment with potent anti-viral drugs has the unwanted effect of inducing resistant strains of HIV that can cause return of high viral burden within patients as well as dissemination throughout populations at risk. Understanding the mechanisms and consequences of treatment failure is vital for epidemic control. This application addresses the statistical problems that arise in studying predictors of virological rebound, and the nature of the virus that rebounds. As resistant strains of HIV become widely dispersed, current therapies will be less effective. For this reason, it is important to classify different genotypic patterns of people with anti-retroviral experience as well as those with newly acquired infection, and to determine the effect of these different classes on the effect of treatment. We describe new and powerful methods for identifying different classes or clusters defined by genotype as well as for determining their effect on response to different treatments. Screening continues to be an important way of monitoring the AIDS epidemic and protecting the blood supply. For this reason, we propose and investigate novel ways of pooling and re-testing blood samples that, theoretically, are both more accurate and cheaper. The potential applications of this method include making it economically feasible to use PCR for screening. Such use has advantages over antibody tests, because PCR detects the presence of virus in newly infected people, before the development of antibody. The long-term consequences of new developments in spread and management of HIV infection must be studies through epidemic surveillance, which is most often achieved by observing AIDS incidence. Because of the long incubation between HIV infection and AIDS, statistical models play a central role in using AIDS incidence for surveillance. We propose analytical techniques required to extract information from the surveillance system, that overcome the effects of the long incubation period. Further, we propose methods to model how treatment is impacting on the epidemic. This methodology in turn may be used to better plan and understand the effect of treatment therapies.